The so-called master-slave system originated from a mechanical master-slave system in which a master robot and a slave robot are mechanically linked so as to work in coordination with each other. The mechanical master-slave system is advantageous in that the operator can have a direct feel of operation, but also disadvantageous in that: the degree of freedom in mechanism design is limited because of geometric restrictions between the operator and the master robot and also between the operator and the slave robot; the system naturally feels heavy to manipulate because the system is driven by human power; and further, the system has trouble in ensuring safety when abnormalities arise.
Therefore, although the mechanical master-slave system is still considered useful, the current mainstream is an electrical master-slave system in which the master robot and the slave robot are electrically interconnected but mechanically separated, and are operable independently of each other. In general, the electrical system can be flexibly controlled with electrical means or by means of software, and can have a mechanism that can be designed with flexibility, and further, the safety of the system can be ensured readily by constructing the system such that the operator is not involved in the working space of a high power actuator.
The electrical master-slave system having these characteristics has been developed mainly for such an application as remote control (i.e., teleoperation), and therefore, the study thereof was carried out mainly focusing on improvements in position and force repeatability, transparency, or communication time delay. An overview description will be provided below regarding basic types of bilateral control for the electrical master-slave system.
First, for convenience of explanation, the equations of motion that represent the dynamics of the master robot and the slave robot are defined by way of example as follows:[Expression 1]JmTfm+τm=Mm,{umlaut over (q)}m+rm  (1);[Expression 2]τs=Ms{umlaut over (q)}s+rs+JsTfs  (2),where fm(t) is a master operating force applied to an operating end of the master robot by the operator at time t, and fs(t) is a slave working force applied to the environment (i.e., a work object) by a working end of the slave robot at the same time t. Furthermore, respectively for the master robot and the slave robot, qm(t) and qs(t) are joint displacements, τm(t) and τs(t) are joint driving forces, Mm(qm) and Ms(qs) are inertia matrices, and rm({dot over (q)}m,qm) and rs({dot over (q)}s,qs) are remainder terms aggregating effects other than inertia. Jm(qm) and Js(qs) are Jacobian matrices representing differential kinematics and satisfying the following relationship:[Expression 3]{dot over (x)}m=Jm{dot over (q)}m  (3);[Expression 4]{dot over (x)}s=Js{dot over (q)}s  (4),where xm(t) and xs(t) are displacements of the operating end of the master robot and the working end of the slave robot in a work coordinate system respectively corresponding to qm(t) and qs(t). Note that symbols, such as “(t)”, which indicate independent variables of a function might be omitted herein.
[Position-Symmetric Bilateral Control]
Position-symmetric bilateral control is bilateral displacement error servo control between the master and the slave. This control eliminates the need for a force sensor, and therefore, renders it possible to readily configure a relatively stable system. In the case where proportional control in the work coordinate system is used, control laws for the master robot and the slave robot are, for example, as shown below:[Expression 5]τm=JmTSf−1Kp(xs−Sp−1xm)  (5);[Expression 6]τs=JsTKp(Sp−1xm−xs)  (6),where Kp is a position control gain. Moreover, Sf is the scale ratio of force from the master robot to the slave robot, and Sp is the scale ratio of displacement from the slave robot to the master robot.
From the master dynamics (1), the slave dynamics (2), the master control law (5), and the slave control law (6), the following expression is obtained.[Expression 7]fm=Jm−T(Mm{dot over (q)}m+rm)+Sf−1Js−T(Ms{umlaut over (q)}srs)+Sf−1fs  (7)In this manner, in the position-symmetric bilateral control, the influence of the master dynamics is added to the master operating force fm as is, and the influence of the slave dynamics and the slave working force fs are also added by a factor of Sf−1.
[Force-Reflecting Bilateral Control]
In force-reflecting bilateral control, a working force sensor for measuring the slave working force fs is disposed at the working end of the slave robot in order to “reflect” the slave working force fs in the force of driving the master. In this case, the master control law is as shown below. Note that the slave control law is the same as in Expression (6) for the position-symmetric bilateral control.[Expression 8]Σm=−JmTSf−1fs  (8)
From the master dynamics (1) and the master control law (8), the following expression is obtained.[Expression 9]fm=JmT(Mm{umlaut over (q)}m+rm)+Sf−1fs  (9)In the case of the force-reflecting bilateral control, as in the case of the position-symmetric bilateral control, the influence of the master dynamics is added to the master operating force fm as is, and the slave working force fs is also added by a factor of Sf−1. On the other hand, the master operating force fm is not influenced by the slave dynamics.
[Force-Reflecting Servo Bilateral Control]
In force-reflecting servo bilateral control, an operating force sensor for measuring the master operating force fm is disposed at the operating end of the master robot, a working force sensor for measuring the slave working force fs is disposed at the working end of the slave robot, and a force error servomechanism is configured on the master side. In this case, the master control law is as shown below.[Expression 10]τm=JmTKf(fm−Sf−1fs)−JmTSf−1fs  (10)The above expression includes force error servo control on the first term of the right-hand side in addition to the master control law (8) for the force-reflecting type. Note that Kf is a force control gain. Moreover, the slave control law is the same as in Expression (6) for the position-symmetric bilateral control.
From the master dynamics (1) and the master control law (10), the following expression is obtained. Note that I is an identity matrix.[Expression 11]fm=(I+Kf)−1Jm−T(Mm{umlaut over (q)}m+rm)+Sf−1fs  (11)
Furthermore, by increasing the force control gain Kf in the above expression to a sufficient degree, the following expression can be obtained.[Expression 12]fm≃Sf−1fs  (12)In this manner, in the case of the force-reflecting servo bilateral control, by sufficiently increasing the force control gain Kf, the influence of the master dynamics on the master operating force fm can be reduced to a negligible degree, so that only the slave working force fs is added to the master operating force fm by a factor of Sf−1. However, for implementation reasons, the stability of bilateral control decreases as the force control gain Kf increases, and therefore, it is difficult to eliminate the influence of the master dynamics on the master operating force fm, so that complete transparency cannot be achieved.
[Parallel Bilateral Control]
In Non-Patent Document 1, Miyazaki et al. propose parallel bilateral control, which is an improvement to the traditional serial connection method for bilateral control. In the case of the parallel type, an operating force sensor for measuring the master operating force fm is disposed at the operating end of the master robot, a working force sensor for measuring the slave working force fs is disposed at the working end of the slave robot, and a parallel displacement error servomechanism is configured by the master and the slave. In this case, the control laws are as shown below:[Expression 13]τm=JmTKp(xd−Sp−1xm)  (13);[Expression 14]τs=JsTSfKp(xd−xs)  (14);[Expression 15]xd=Kf(fm−Sf−1fs)  (15).Note that Xd(t) is a target displacement for each of the working end of the slave robot and the scaled operating end of the master robot at time t in the work coordinate system.
From the master dynamics (1), the slave dynamics (2), the master control law (13), the slave control law (14), and the target displacement calculation (15), the following expression can be obtained.
                                              ⁢                  [                      Expression            ⁢                                                  ⁢            16                    ]                                                                              f          m                =                                                            (                                  I                  +                                      2                    ⁢                                          K                      p                                        ⁢                                          K                      f                                                                      )                                            -                1                                      ⁢                                          J                m                                  -                  T                                            ⁡                              (                                                                            M                      m                                        ⁢                                                                  q                        ¨                                            m                                                        +                                      r                    m                                                  )                                              +                                                    (                                  I                  +                                      2                    ⁢                                          K                      p                                        ⁢                                          K                      f                                                                      )                                            -                1                                      ⁢                          S              f                              -                1                                      ⁢                                          J                s                                  -                  T                                            ⁡                              (                                                                            M                      s                                        ⁢                                                                  q                        ¨                                            s                                                        +                                      r                    s                                                  )                                              +                                                    (                                  I                  +                                      2                    ⁢                                          K                      p                                        ⁢                                          K                      f                                                                      )                                            -                1                                      ⁢                                          K                p                            ⁡                              (                                                                            S                      p                                              -                        1                                                              ⁢                                          x                      m                                                        +                                      x                    s                                                  )                                              +                                    S              f                              -                1                                      ⁢                          f              s                                                          (        16        )            Furthermore, by increasing the force control gain Kf in the above expression to a sufficient degree, the following expression can be obtained.[Expression 17]fm≃Sf−1fs  (17)The advantage of the parallel bilateral control is that phase lag is reduced by providing the master control law and the slave control law in parallel, resulting in bilateral control with increased stability. However, in the case of the parallel bilateral control, the master operating force fm is influenced by both the master dynamics and the slave dynamics, as can be seen from the first and second terms of the right-hand side of Expression (16). Moreover, in the case of the parallel bilateral control, even a spring constant term, which is not included in the original dynamics, is added to the master operating force fm, as can be seen from the third term of the right-hand side of Expression (16). Such influences can be reduced to a negligible degree by increasing the force control gain Kf, but for implementation reasons, even the increased stability of the bilateral control can be weakened as the force control gain Kf increases, and therefore, even the parallel bilateral control cannot achieve complete transparency.
[Force-Projecting Bilateral Control]
The basic types of bilateral control, including the position-symmetric type, the force-reflecting type, the force-reflecting servo type, and the parallel type, have been described so far, and conventional bilateral control, including these types, has Problems 1 through 10 as follows:
[Problem 1] A problem common among the force-reflecting type, the force-reflecting servo type, and the parallel type.
Information about the slave working force fs is required for control, and therefore, difficulty is found in application to a system in which the working force sensor cannot be mounted on the slave robot.
[Problem 2] A problem common between the position-symmetric type and the force-reflecting type.
Control drives the system in accordance with displacement error of the master robot, and therefore, it is necessary to set the inertia and the friction of the master robot as low as possible, such that displacement error of the master robot can be readily generated by human power, i.e., high backdrivability is ensured. Accordingly, it is requisite for the master robot to be a powerless and fragile mechanism with a low reduction ratio.
[Problem 3] A problem common among the position-symmetric type, the force-reflecting type, the force-reflecting servo type, and the parallel type.
Control causes the master dynamics to influence the master operating force fm, and therefore, for improvements to operability as well, it is necessary to set the inertia and the friction of the master robot as low as possible. Accordingly, it is desirable for the master robot to be a powerless and fragile mechanism with a low reduction ratio.
[Problem 4] A problem common between the force-reflecting type and the force-reflecting servo type.
Control is based on the norm of transparency and therefore does not cause the slave dynamics to influence the master operating force fm, so that the operator's skills are not expected to be improved by taking advantage of feeling the sense of the slave dynamics, and further, slave robot operation is not expected to become either more efficient or optimized.
[Problem 5] A problem common between the force-reflecting servo type and the parallel type.
Despite control being based on the norm of transparency, transparency might not be achieved if necessary stability is sought to be achieved because transparency and stability are in a trade-off relationship.
[Problem 6] A problem common among the force-reflecting type, the force-reflecting servo type, and the parallel type.
If the working force sensor disposed on the slave robot contacts a hard environment, there is a risk that the system might be destabilized (a problem with contact stability of the slave robot). To prevent this, it is conceivable to decrease the force control gain Kf to a sufficient degree, or switch control laws in accordance with whether the slave robot is in contact with the environment, but the former reduces operability and transparency, whereas the latter results in complex implementation.
[Problem 7] A problem common among the position-symmetric type, the force-reflecting type, the force-reflecting servo type, and the parallel type.
The slave robot and the master robot are always connected bidirectionally, and therefore, there is a risk that unstable behavior might be excited in the system solely by an external force −fs applied to the slave robot, even if the operator is not manipulating the master robot.
[Problem 8] A problem common among the position-symmetric type, the force-reflecting type, the force-reflecting servo type, and the parallel type.
A command value for the slave robot is position-related, and the slave dynamics need to be cancelled by positional control, which imposes a large burden on the control system. In addition, the control law based on the positional control does not necessarily allow another control law to be superimposed thereon.
[Problem 9] A problem common among the force-reflecting type, the force-reflecting servo type, and the parallel type.
In controlling the position of the slave robot, if the output of a slave actuator becomes insufficient, so that slave driving force r, is saturated, error between master displacement and slave displacement might increase, resulting in reduced operability.
[Problem 10] A problem common among the position-symmetric type, the force-reflecting type, the force-reflecting servo type, and the parallel type.
When positional control in the work coordinate system is applied to the slave robot, a singularity problem might arise, so that control failure might occur when the posture of the slave robot approaches a singularity.
As new bilateral control capable of neatly solving these problems, the present inventor proposes the basic configuration of “force-projecting bilateral control” in Patent Document 1. In the force-projecting type, an operating force sensor for measuring the master operating force fm is disposed at the operating end of the master robot, and the measured master operating force fm is “projected” to the slave driving force τs. In the force-projecting bilateral control, the master control law and the slave control law are, for example, as shown below:[Expression 18]τm=JmTKp(Spxs−xm)  (18);[Expression 19]τ6=JdTSffm  (19).
From the slave dynamics (2) and the slave control law (19), the following expression can be obtained.[Expression 20]fm=Sf−1Js−T(Ms{umlaut over (q)}s+rs)+Sf−1fs  (20)In this manner, in the case of the force-projecting bilateral control, the influence of the slave dynamics and the slave working force fs are added to the master operating force fm by a factor of Sf−1. That is, the force-projecting bilateral control is an approach to measure the master operating force fm applied to the master robot by the operator, rather than the slave working force fs applied to the environment (i.e., a work object) by the slave robot, and allow the master to pass force information forward to the slave while allowing the slave to feed displacement information back to the master.
The force-projecting bilateral control has Characteristics 1 through 10 as shown below:
[Characteristic 1] Applicable to even a system in which the working force sensor cannot be mounted on the slave robot, because no information about the slave working force fs is needed.
[Characteristic 2] Not requiring the master robot to have backdrivability because the system is driven by the master operating force fm applied to the master robot by the operator, rather than in accordance with displacement error of the master robot, so that the master robot can be rendered as a mechanism which is robust enough to withstand human power, and is also highly accurate and powerful.
[Characteristic 3] Being control that does not cause the master dynamics to influence the master operating force fm, so that there is no need to set the inertia and the friction of the master robot low in order to improve operability. Accordingly, for a different reason from that for Characteristic 2, the master robot can be rendered as a mechanism which is robust enough to withstand human power, and is also highly accurate and powerful.
[Characteristic 4] Being control that is not based on the norm of transparency and therefore causes the slave dynamics to influence the master operating force fm, so that the operator's skills are expected to be improved by taking advantage of feeling the sense of the slave dynamics, and further, slave robot operation is expected to become more efficient and optimized.
[Characteristic 5] Being control that is based on the norm of “projectivity” as defined by the present inventor in Patent Document 2, rather than transparency; projectivity is not in a trade-off relationship with stability, and therefore can be achieved with a necessary accuracy independently of stability.
[Characteristic 6] Being control that allows the slave robot to feed displacement information, rather than force information, back to the master robot, so that there is no problem with contact stability of the slave robot.
[Characteristic 7] No risk of unstable behavior being excited in the system solely by an external force −fs applied to the slave robot because the connection from the master robot to the slave robot is terminated (i.e., the connection therebetween changes from bilateral to unilateral) unless the operator applies the master operating force fm to the master robot.
[Characteristic 8] The command value for the slave robot is related to drive power (force and torque), rather than position-related, which facilitates the implementation of the slave control law, and imposes little burden on the control system. The control is based on drive power, and therefore, any type of control based on drive power can be superimposed on the slave control law.
[Characteristic 9] The master robot is rendered as a mechanism which is robust enough to withstand human power, so that even if the output of the slave actuator becomes insufficient in controlling the power of driving the slave robot, resulting in saturation of the slave driving force τs, there is little possibility that the output of a master actuator is saturated in positional control of the master robot, so that master displacement and slave displacement can be matched with a sufficient accuracy, resulting in no reduction of operability.
[Characteristic 10] The slave robot is not position-controlled but is controlled in terms of drive power, and therefore, no singularity problem occurs even if the control in the work coordinate system is applied, so that control failure does not occur even if the posture of the slave robot approaches a singularity.